An online course participant had a question about a rhombus construction that failed the drag test. The failure occurred because vertex C was a point on a line, and the opposite vertex was an intersection of a circle with the line. Dragging point C along the line could cause the intersection to coincide with the point being dragged -- and you no longer have a rhombus when two of its vertices coincide!

I made a sketch to demonstrate how and why the problem occurs, and to give one sample solution using reflection. If you've ever had this problem happen to you, you may find this sketch helpful. You'll find the sketch here:

I also present a challenge: to find other solutions using rotation, dilation, or translation instead of reflection.